PhD in Computer Science, specialized in Computational Geometry and Computer Algebra, focusing on problems appearing in visualization tasks and robotics design, with additional interests in Machine Learning.
George Krait, a mathematician and Computer scientist (Computational Geometry) with additional interests in Machine learning. I work as a Research Engineer at the French Institute for Research in Computer Science and Automation, France.
In my Ph.D. program, I was working in (efficiently) plotting singular plane curves preserving properties such as topology . Isolating the singularities of a plane curve is the first step towards computing its topology. For this, numerical methods are efficient but not certified in general. The goal of my work is to develop certified numerical algorithms for isolating the singularities. In order to do so, we restrict our attention to the special case of plane curves that are projections of smooth curves in higher dimensions. This type of curves appears naturally in robotics applications and scientific visualization. In this setting, we show that the singularities can be encoded by a regular square system whose solutions can be isolated with certified numerical methods. Our analysis is conditioned by assumptions that we prove to be generic using Transversality theory . We also provide a semi-algorithm to check their validity. Finally, we present experiments in visualization and robotics, some of which are not reachable by other methods, and discuss the efficiency of our method.
In my master's program at TU Kaiserslautern, Germany I worked in computing a minimal standard basis of an algebraic object called Algebroid curve. I implemented the algorithm and its applications in Singular which is a computer algebra system for polynomial computations.
- Supervised learning (parametric/non-parametric algorithms, support vector machines, kernels, neural networks).
- Unsupervised learning (clustering, dimensionality reduction, recommender systems, deep learning).
- Best practices in machine learning (bias/variance theory; innovation process in machine learning and AI).
Indexes and Transactions, Constraints and Triggers,Views and Authorization
Relational Databases, Relational Algebra, Design Theory and Unified Modeling Language
- Implement translation algorithms from the fragment identifier to Cubicle input language
- Coupling TLAPS with automatic verification tools using these translations
- Generating a documentation for the techniques and the produced codes
Tutoring courses in:
- Scientific Programming Languages
- Rational Database
- Pursuing research in modeling the projections of 3D (even higher!) curves.
- Using efficient symbolic and certified numerical tools for visualization & robotics purposes
- Designing & implementing related algorithms
Specialization: Geometry, Algebra and Computer Algebra
Thesis context: Development and implementation of algorithms regarding curves defined with infinite series
Undertaking an intensive Bachelor program of Pure & Applied Mathematics courses
KAAD Scholarship for pursuing master degree at TU Kaiserslautern, Germany
Selected for the Syrian team in the International Mathematical Olympiads for University students.
Top ten ranking in the Syrian National Olympiads of Mathematics for University Students.